Modern corals are colonial; meaning each structure is actually made up of the shells of masses of tiny animals. Some members of the group Rugosa were instead solitary, growing orders of magnitude larger than any single living coral. Corals are cnidarians, a group that also includes jellyfish.
The tip of the ‘horn’ was shallowly buried in ocean floor sediments. This would lead to corals falling over on occasion due to strong currents; the animal would then build its shell towards the ‘new up’, which is why some rugose coral fossils are bent rather than straight shelled.